An investigation of turbulent developing flow at the entrance to a smooth pipe

An attempt is made to explain the flow regimes at the entry region of a pipe. Developing turbulent flow was examined and three theoretical models were evolved to explain the three most important regimes: the region of flat plate flow, the region of transition from flat plate to pipe flow, and the region of boundary layer interaction. The model for the flat plate flow was based on the velocity power law but experimental data showed that the exponent was not constant as generally assumed. There was good agreement between the theoretical models and the experimental data for the boundary layer development.

A simple empirical formula was obtained from which it is possible to predict the length of the entry region. The onset of the increase in turbulence intensity at the core, which marks the start of transition from flat plate flow to pipe flow, seems to occur at a particular Reynolds number, based on distance into pipe, of about 3.15×10⁶. This figure may vary with inlet flow condition.     

Sonic annular jet in a counterstreaming supersonic flow

When sonic annular jets encounter a supersonic flow, two interaction regimes are possible with open or closed central separation regions. When the flow regimes change, there is an abrupt change in the separation of the shock wave from the nozzle and of the pressure in the central separation region, and hysteresis is also observed. The flow regimes with open central separation region are stationary and can be calculated numerically on the basis of Euler's equations fairly accurately.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–180, September–October, 1979.     

On Disturbance Propagation in Internal-Flow Boundary Layers

The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near the nozzle outlet or by deforming the channel walls is studied. In these conditions, the interaction process is described by a system of Burgers equations with retarded arguments. Numerical solutions of this system are obtained for symmetric and antisymmetric perturbations of the channel walls.     

Regime diagram of the development of long-wave near-wall disturbances in a hypersonic boundary layer

A regime diagram of the development of slow near-wall disturbances induced by an unsteady self-induced pressure perturbation in a hypersonic boundary layer is constructed for a disturbance wavelength greater than the boundary layer thickness. It is shown that the main factors shaping the perturbed flow are the gas enthalpy near the body surface, the intensity of the viscous-inviscid interaction, and the nature (sub- or supersonic) of the main part of the boundary layer. Nonlinear boundary-value problems are formulated for regimes in which the near-wall boundary layer region plays a decisive role. Numerical and analytical solutions are obtained in the linear approximation. It is shown that intensification of the viscous-inviscid interaction or an increase in the role of the supersonic main region of the boundary layer impart generally supersonic properties to the main part of the boundary layer, i.e. the upstream propagation of the disturbances is damped and the disturbance growth downstream becomes more intense. Damping of the viscous-inviscid interaction and an increase in the role of the subsonic main part of the boundary layer have the opposite effect. Surface cooling increases the effect of the main part of the boundary layer on the formation of pressure disturbances and surface heating leads to an increase in the effect of the near-wall boundary layer region. It is also shown that for the regimes considered disturbances propagate in a direction opposite to that of the free stream from the turbulent flow region located downstream of the local disturbance development region.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 59–71. Original Russian Text Copyright © 2004 by Bogolepov and Neiland.     

Wave-flow theory for a thin viscous liquid layer

On the basis of a simplified system of equations we study the process of development and stability of wave flows in a thin layer of a viscous liquid. Any unstable disturbance of the laminar flow grows and leads to the establishment of the wave regime. The time to establish the flow changes little for large flow rates, but increases sharply with reduction of the flow rate. Given the same amplitudes of the initial disturbances, the optimum regimes which provide the greatest flow rate in a layer of given average thickness develop more rapidly than the other regimes. All the wave regimes are unstable to disturbances in the form of traveling waves. With moderate flow rates, the optimum regimes will be most stable to near-by disturbances.Strictly periodic wave flows in a thin layer of a viscous liquid under the influence of the gravity force were calculated in [1], Various flow wave regimes which differ in wavelength can theoretically be established for a given liquid flow rate. In particular, there is a wavelength for which the flowing layer exhibits minimum average thickness (and maximum flow rate for a given average thickness). These optimum regimes correspond closely to the experimental data [2]; however, with regard to calculation technique these regimes are no different from the others. In the following we make a comparison of the wave regimes on the basis of the nature of their development and stability.     

Application of photogrammetry to surface flow visualization

The construction of three-dimensional surface flow fields is an extremely difficult task owing largely to the fragmented information available in the form of 2D images. Here, the method of photogrammetric resection based on a comprehensive camera model has been used to map oil flow visualization images on to the surface grid of the model. The data exported in the VRML format allow for user interaction in a manner not possible with 2D images. The technique is demonstrated here using the surface oil flow visualization images of a simplified landing gear model at low speed in a conventional wind tunnel without any specialized rigs for photogrammetry. The results are not limited to low-speed regimes and show that this technique can have significant impact on understanding the flow physics associated with the surface flow topology of highly three-dimensional separated flows on complex models.     

Transition between the regular and Mach shock interaction regimes initiated by a temperature disturbance

The results of searching numerically temperature disturbances which make it possible to convert flow from the steady-state Mach to regular shock interaction when both regimes may coexist simultaneously are given. The flow sensitivity to the temperature variations is calculated by solving the adjoint equations. The control perturbation is sought using gradient methods. The numerical experiments show that transition from the regular to Mach regime can be realized over the Mach number range from 3.45 to 6 by means of an increase in the temperature. Transition from the Mach to regular regime requires to decrease the temperature, it is possible for moderate Mach numbers and cannot be realized for the higher Mach numbers.     

Study of the Interaction of a Streamwise-Oscillating Shock with the Boundary Layer on a Flat Plate

The distinctive features of the flow in the region of interaction between an oscillating shock and a flat-plate boundary layer are studied for the laminar, transitional, and turbulent flow regimes. The flow patterns and the pressure and heat transfer distributions in the interaction region are analyzed at different intensities, frequencies, and amplitudes of the oscillating shock. The results of the interaction of oscillating and steady shocks with the flat-plate boundary layer are compared.     

Hysteresis phenomenon at interaction of shock waves generated by a cylinder array

This paper describes investigations of the interaction between bow shock waves generated by cylindrical bodies in a supersonic flow. Numerical simulations are performed using the inviscid Euler equations for cylinders whose axes are parallel to each other and normal to the flow direction. Mostly an infinite periodical cylinder array is considered, but the case of two cylinders is also briefly discussed. Three different regimes of the shock wave interaction, a regular interaction, a Mach interaction, and a choked flow, have been observed for the flow through the periodical cylinder array. In the case of the flow around two bodies, the choked flow is replaced by a regime with a collective bow shock. The transition between different flow regimes is studied by varying the inflow Mach number or the distance between the cylinders. A hysteretic behavior at the transition between the regular and Mach interactions has been observed. The transition is governed by the theoretical detachment and von Neumann criteria based on the local shock wave inclination at the interaction point.     

Simulation of the Effect of the Freestream Turbulence Parameters on the Boundary Layer of a Curvilinear Airfoil

Modified variants of differential turbulence models which make it possible continuously to calculate both the entire flow region with laminar, transition and turbulent regimes and local low Reynolds number zones are proposed for investigating the flow and heat transfer in the boundary layers developing in compressible gas flow past curvilinear airfoils. The effect of the intensity and scale of free-stream turbulence and their variability along the outer boundary layer edge, as well as the combined action of the turbulence intensity and the streamwise pressure gradient in flow past blade profiles, on the heat transfer and near-wall turbulence characteristics is analyzed. The numerical results are compared with experimental and theoretical data.     

Interaction Between a Time-Dependent Laminar Boundary Layer and an Inviscid Subsonic Flow Near a Region of Local Energy Supply

The results of numerical modeling of the time-dependent flows of a viscous heat-conducting gas occurring in the region of interaction between an external inviscid flow and a laminar boundary layer near a zone of local energy supply at high subcritical Reynolds numbers are presented. The solution of the Navier-Stokes equations is constructed on the basis of the method of matched asymptotic expansions. Numerical solutions of the nonlinear boundary-value problem describing the flow in the wall region of the boundary layer are given in similarity variables. It is shown that time- and space-localized energy supply results in the formation of a self-consistent flow disturbance, whose downstream propagation is accompanied by a disturbance amplitude growth during a short time interval, even after the energy supply has stopped. Calculations of the flows induced by two heat sources placed in tandem make it possible to conclude that the time lag for the second energy supply zone and the distance between the sources can be so chosen that superposition of the disturbances induced by the first and second sources leads, due to nonlinear effects, to a considerable increase in the amplitude of the total flow disturbance.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 64–75.Original Russian Text Copyright © 2005 by Kazakov.     

Supersonic rarefied gas flow through a wire grid

The direct simulation Monte Carlo method is used to study a plane-parallel supersonic gas flow through a grid formed by a series of parallel infinite cylinders. Characteristic features of the shock disturbance formation during the interaction of a supersonic flow with a permeable grid and the effect of this disturbance on the flow parameters behind the grid are revealed. The boundaries of the domain of supersonic flow breakup ahead of the grid and the laws of the total momentum loss on the grid are obtained. Kinetic and energetic characteristics of the flow behind the grid are determined.     

Interaction of a Streamwise Vortex with an Oblique Shock Wave

Interaction of a supersonic streamwise vortex with an oblique shock wave is considered. A mathematical model of the streamwise vortex is constructed. Three interaction regimes (weak, moderate, and strong) are found. It is shown numerically that vortex breakdown is possible in the case of strong interaction. The influence of the governing parameters on the interaction type is studied. It is shown that the main effect on the interaction type is exerted by the streamwise velocity and angle of the wedge forming the shock wave. The effect of splitting of the primary vortex on the shock wave in the case of moderate and strong interaction regimes is found.     

Interaction between a shock wave and a longitudinal low-density gas layer

The problem of the interaction between a shock wave and a semi-infinite longitudinal plane layer or a cylindrical channel of finite thickness filled with a low-density gas is studied on the basis the Euler equations. The flow gasdynamics, including qualitatively new, regular and irregular, interaction regimes, are described. New gasdynamic flow elements, such as high-pressure jets with an internal wave structure and layered vortices, are found to exist. It is revealed that the gasdynamic precursor growth is decelerated at long time intervals, due to the flow chocking effect and the vorticity development behind its front.     

Injection and coalescence of bubbles in a quiescent inviscid liquid

Time periodic generation and coalescence of bubbles by injection of a gas at a constant flow rate through an orifice at the bottom of a quiescent inviscid liquid is investigated numerically using a potential flow formulation. The volume of the bubbles is determined for different values of a Weber number and a Bond number. Single bubbling and different regimes of coalescence are described by these computations. The numerical results show qualitative agreement with well-known experimental results for liquids of low viscosity, suggesting that bubble interaction and coalescence following gas injection is to a large extent an inviscid phenomenon for these liquids, many aspects of which can be accounted for without recourse to wake effects or other viscosity-dependent ingredients of some current models.     

Interaction of a heavy fluid flow in a channel with a transverse jet barrier

An experimental and numerical analysis of the interaction between a plane horizontal water flow in a rectangular channel (free water current) and a plane thin water jet (water jet curtain) is presented; the jet flows out vertically from either a slot nozzle in the bottom of the channel or the crest of a rigid spillway at a velocity appreciably (several times) greater than the water velocity in the channel. Numerical calculations were carried out using the STAR-CD software package preliminarily tested against the experimental data obtained. The dependence of the water level in the channel at a certain distance ahead of the jet barrier on the main jet parameters and the water flow rate in the horizontal channel is studied. It is found that in the region of the interface between the flows both steady and unsteady (self-oscillatory) flow patterns can be realized. Steady stream/jet interaction patterns of the “ejection” and “ejection-spillway” types are distinguished and a criterion separating these regimes is obtained. The notion of a rigid spillway equivalent to a jet curtain is introduced and an approximate dependence of its height on the relevant parameters of the problem is derived. The possibility of effectively controlling the water level ahead of a rigid spillway with a sharp edge by means of a plane water jet flowing from its crest is investigated. The boundary of transition to self-oscillation interaction patterns in the region of the flow interface is determined. The structure of these flows and a possible mechanism of their generation are described. Within the framework of the inviscid incompressible fluid model in the approximate formulation for a “thin” jet, an analytical dependence of the greatest possible depth of a reservoir filled with a heavy fluid at rest and screened by a vertical jet barrier on the jet parameters is obtained.     

Development of slow disturbances in a hypersonic boundary layer

The mechanisms of development of slow time-dependent disturbances in the wall region of a hypersonic boundary layer are established and a diagram of the disturbed flow patterns is plotted; the corresponding nonlinear boundary value problem is formulated for each of these regimes. It is shown that the main factors that form the disturbed flow are the gas enthalpy near the body surface, the local viscous-inviscid interaction level, and the type, either subsonic or supersonic, of the boundary layer as a whole. Numerical and analytical solutions are obtained in the linear approximation. It is established that enhancement of the local viscous-inviscid interaction or an increased role for the main supersonic region of the boundary layer makes the disturbed flow by and large “supersonic”: the upstream propagation of the disturbances becomes weaker, while their downstream growth is amplified. Contrariwise, local viscous-inviscid interaction attenuation or an increased role for the main subsonic region of the boundary layer has the opposite effect. Surface cooling favors an increased effect of the main region of the boundary layer while heating favors an increased wall region effect. It is also found that in the regimes considered disturbances travel from the turbulent flow region downstream of the disturbed region under consideration counter to the oncoming flow, which may be of considerable significance in constructing the nonlinear stability theory.     

A minimal model for flow control on an aerofoil using a poro-elastic coating

A minimal model is obtained for vortex-shedding from an aerofoil with a porous coating of flow-compliant feather-like actuators, in order to better understand this passive way to achieve flow control. This model is realized by linearly coupling a minimal-order model for vortex-shedding from the same aerofoil without any such coating with an equation for the poro-elastic coating, here modelled as a linear damped oscillator. The various coefficients in this model, derived using perturbation techniques, aid in our understanding of the physics of this fluid–structure interaction problem. The minimal model for a coated aerofoil indicates the presence of distinct regimes that are dependent on the flow and coating characteristics. The models and the parametric studies performed provide insight into the selection of optimal coating parameters, to enable flow control at low Reynolds numbers.     

Interference of a Bow Shock with an Oblique Shock and an Isentropic Compression Wave

The features of the flow in the zone of interaction between a plane bow shock and an oblique shock or an isentropic compression wave are studied. The limiting interaction regimes are considered analytically, the similarity conditions are formulated, and the limiting values of the flow parameters are determined for the high-pressure compressed gas jet formed in the interference and for the body surface. On the basis of a numerical solution of the Euler equations the flow specifics in the neighborhood of the spreading line on the body are determined and ways of reducing the dynamic and thermal loadings on this line are proposed.